The letter D has how many lines of symmetry?

2011

The letter D has how many lines of symmetry?

  1. A.

    One

  2. B.

    Two

  3. C.

    Three

  4. D.

    None of these

Attempted by 5 students.

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Correct answer: A

A line of symmetry of a figure is a straight line along which the figure can be folded so that the two halves coincide exactly as mirror images of each other; depending on its shape, a figure can have zero, one, two, or more such lines.

The capital letter D is formed by a straight vertical stroke joined to a curved arc that bulges outward on one side. Folding the letter along a horizontal line through the midpoint of the vertical stroke maps the upper half of the curve exactly onto the lower half, and the straight stroke maps onto itself — so this horizontal line is a valid axis of symmetry. Folding along any vertical line does not work, because one side of the letter is a straight edge while the other is a curve, so the two sides never coincide; a diagonal line fails for the same reason.

Checking against related capital letters confirms the pattern: B, C, and E also fold matching only along a horizontal axis, even though they are built differently — C is a single curved arc, E is made of straight strokes only, and B combines a straight edge with two curves — the shared property is top-to-bottom mirror symmetry, not left-right symmetry. Letters that ARE left-right mirror images of themselves, such as A, M, T, and U, instead match along a vertical axis. D therefore has exactly one line of symmetry — the horizontal axis through its middle.

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